Fluctuations in an Evolutional Model of Two-Dimensional Young Diagrams

TL;DR

This paper investigates the non-equilibrium fluctuations in a dynamic model of two-dimensional Young diagrams, deriving linear stochastic PDEs and showing their invariant measures match static Gaussian limits.

Contribution

It introduces a new analysis of non-equilibrium fluctuations in Young diagram dynamics and derives associated linear stochastic PDEs with Gaussian invariant measures.

Findings

Derived linear stochastic PDEs for the fluctuation limits.

Invariant measures are Gaussian and match static fluctuation limits.

Established connection between dynamic and static fluctuation behaviors.

Abstract

We discuss the non-equilibrium fluctuation problem, which corresponds to the hydrodynamic limit established in \cite{FS}, for the dynamics of two-dimensional Young diagrams associated with the uniform and restricted uniform statistics, and derive linear stochastic partial differential equations in the limit. We show that their invariant measures are identical to the Gaussian measures which appear in the fluctuation limits in the static situations.